Abstract

Automatic detection of symmetries, regularity, and repetitive struc- tures in 3D geometry is a fundamental problem in shape analysis and pattern recognition with applications in computer vision and graphics. Especially chal- lenging is to detect intrinsic regularity, where the repetitions are on an intrinsic grid, without any apparent Euclidean pattern to describe the shape, but rising out of (near) isometric deformation of the underlying surface. In this paper, we employ multidimensional scaling to reduce the problem of intrinsic structure de- tection to a simpler problem of 2D grid detection. Potential 2D grids are then identi fied using an autocorrelation analysis, refined using local fitting, validated, and finally projected back to the spatial domain. We test the detection algorithm on a variety of scanned plaster models in presence of imperfections like missing data, noise and outliers. We also present a range of applications including scan completion, shape editing, super-resolution, and structural correspondence.